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Statistical Papers

, Volume 60, Issue 6, pp 1849–1882 | Cite as

Preliminary test and Stein-type shrinkage ridge estimators in robust regression

  • M. Norouzirad
  • M. ArashiEmail author
Regular Article

Abstract

A statistician may face with a dataset that suffers from multicollinearity and outliers, simultaneously. The Huberized ridge (HR) estimator is a technique that can be used here. On the other hand, an expert may claim that some/all the variables should be removed from the analysis, due to inappropriateness, that imposes a prior information that all coefficients equal to zero (in the form of a restriction) to the analysis. In such situations, one may consider the HR estimation under the subspace restriction. In this paper, we introduce some improved estimators for verifying this claim. They are employed to improve the performance of the HR estimator in the multiple regression model. Advantages of the proposed estimators over the usual HR estimator are demonstrated through a Monte Carlo simulation as well as two real data examples.

Keywords

M-estimation Multicollinearity Outliers Preliminary test Ridge regression Stein-type Shrinkage 

Supplementary material

362_2017_899_MOESM1_ESM.pdf (1.2 mb)
Supplementary material 1 (pdf 1182 KB)

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Statistics, School of Mathematical SciencesShahrood University of TechnologyShahroodIran

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